1. Warm Up
1. What percent of 60 is 18?
2. What number is 44% of 6?
3. Find mWVX. 30
2.64
104.4

2. Objectives Apply properties of arcs. Apply properties of chords.
A central angle is an angle whose vertex is the center of a circle.
An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.

4. Example 1: Data Application
The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF.
mKLF = 360° – mKJF
mKJF = 0.35(360)
= 126
mKLF = 360° – 126°
= 234

5. Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.
Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure ST  UV.

6. Example 2: Using the Arc Addition Postulate
Find mBD.
mBC = 97.4
Vert. s Thm.
mCFD = 180 – (97.4 + 52)
= 30.6
∆ Sum Thm.
mCD = 30.6
mCFD = 30.6
mBD = mBC + mCD
Arc Add. Post.
= 97.4 
Substitute.
Simplify.
= 128

8. Example 3A: Applying Congruent Angles, Arcs, and Chords
TV  WS. Find mWS.
TV  WS
 chords have  arcs.
mTV = mWS
Def. of  arcs
9n – 11 = 7n + 11
Substitute the given measures.
2n = 22
Subtract 7n and add 11 to both sides.
n = 11
Divide both sides by 2.
mWS = 7(11) + 11
Substitute 11 for n.
= 88°
Simplify.

10. Example 4: Using Radii and Chords
Find NP.
Step 1 Draw radius RN.
RN = 17
Radii of a  are .
Step 2 Use the Pythagorean Theorem.
SN2 + RS2 = RN2
SN = 172
Substitute 8 for RS and 17 for RN.
SN2 = 225
Subtract 82 from both sides.
SN = 15
Take the square root of both sides.
Step 3 Find NP.
NP = 2(15) = 30
RM  NP , so RM bisects NP.

11. Lesson Quiz: Part I
1. The circle graph shows the types of cuisine available in a city. Find mTRQ.
158.4

12. Lesson Quiz: Part II
Find each measure.
2. NGH
139
3. HL 21

13. Lesson Quiz: Part III
4. T  U, and AC = Find PL to the nearest tenth.
 12.9